Method and device for generating a digital lookup table for printing inks in image reproduction equipment

ABSTRACT

The subject of the invention is a method and a device for generating a digital lookup table for printing inks in image reproduction equipment. Color scan values obtained by photoelectric scanning of an original are used for this purpose. The full colors of the three printing inks and white are measured. Model colors are determined which are in as linear as possible a relationship to the printing inks. This is achieved by a position of the chromaticity range of the print scale such that the primary stimuli of the model colors in the chromaticity diagram are each on one beam of the trajectories of the scale colors through the white point while the triangle set up between the primary stimuli encloses the chromaticity range of the print scale. The scale division of the primary stimuli is adjusted with a cube root to the printing inks. The number of fields to be scanned is determined on the basis of the measured values of the space diagonals. A cubic spline interpolation follows to generate the lookup table.

BACKGROUND OF THE INVENTION

The invention relates to a method for generating a digital lookup tablefor printing inks in image reproduction equipment using color scanvalues obtained by photoelectric scanning of an original.

The basis for generation of a transformation table for the primarycolors "RGB" into the complementary colors "CMYK" is spectrophotometricmeasurement of a color scale generated with that process (e.g. Offset,Euroskala, coated paper) for which this table is later to apply. Withunlimited expenditure, it would be possible to thereby obtain bymeasurement the right field for every required color stimulus from ascale with 1% gradation of the printing inks, i.e. 100*100*100 colorfields. A method of this type would provide, if the color range of thescale is not always exceeded, the formula for the complementary colors"CMYK" accurate to 1%. Highly saturated hues have no correspondingfield. In addition, one million measurements are impracticable forgenerating a table.

A color correction device for image reproduction equipment is known withwhich digitalized color density values of individual color separationsobtained by photoelectric scanning are converted into complementarycolor density values. With the complementary color density values it ispossible to obtain color separation negatives. The complementary colordensity values are color-corrected using correction data filed in amemory and addressable and outputtable by the color density values. Agray component is determined from the color density values. This isachieved by comparing the color density values. The gray component isprocessed by comparison with a predetermined white light value to obtainan equivalent gray value with which a memory is addressed that containsa specific gray value for each complementary color density value. Bysubtracting the gray components from the color density values,complementary color density values are generated. The variouscomplementary color density values are each combined with an associatedspecific gray value. Corrections to the chromatic component and to thegray component independently of one another permit a saving of memorycapacity for the conversion table (German patent DE-PS 30 15 396).

One of the objects underlying the invention is to develop a method forgeneration of a digital lookup table (memory table) of complementaryprinting inks for image reproduction equipment using standardized colorscan values obtained by photoelectric scanning of an original, e.g. EBUred, green, blue. With the method of the invention a lookup table can beproduced from a few measurement fields that is sufficiently accurate fordetermining the proportions of printing inks. In addition,non-reproducible color stimuli must be adapted to useful substitutevalues.

The object is substantially achieved in accordance with the invention inthat the full colors of the three printing inks and white are measuredby scanning of corresponding originals, in that model colors aredetermined which are in as linear as possible a relationship to theprinting inks by means of a position of the chromaticity range of theprint scale such that the primary stimuli of the model colors in thechromaticity diagram are each on one beam of the trajectories of thescale colors through the white point while the triangle set up betweenthe primary stimuli encloses the chromaticity range of the print scale.The scale division of the primary stimuli is adjusted with the cube rootto a linear gradation of the printing inks. The space diagonals of theprinting inks as a function of the model colors are used to determinethe number of fields to be scanned, scan values of which are furtherprocessed by cubic spline interpolation with a higher number of supportpoints in order to generate the lookup table. The values of the modelcolors are each stored as a function of the printing ink values.

A lookup table of the printing inks as a function of the model colors ispreferably generated from the stored lookup table. The latter table isused in the reproduction equipment to determine the proportions ofprinting inks for the original artwork measured values.

A substantial element of the invention is based on the setup of acomputation model whose coordinate axes tally as closely as possiblewith the axes of the print scale (cyan, magenta and yellow). A componentof the model color space depends in largely linear form on one and oneonly printing ink. The CIE-XYZ color space of the International LightingCommission does not--unlike the model color space describedabove--fulfill these requirements, since the directions of itscoordinate axes do not even approximately tally with those of theprimary stimuli of the print scale. Particularly unfavorable is the factthat identically sized color intervals at different points on the printscale are reproduced on variously sized differences in the CIE-XYZ colorspace. The aforementioned substitute colors C_(t), M_(t) and Y_(t)describe the printing inks approximately and can be advantageouslyconverted as a group into values of the CIE-XYZ color space. Therelationship C_(t) =1-R makes the substitute color stimulus C_(t)proportional to the color stimulus C_(s). Weighting with the cube rootlinearizes the dependence of the model color on the printing ink. Theconversion between the coordinates of the RGB color space and of theCIE-XYZ color space and vice versa is achieved in each case with atransformation matrix that is known per se (Richter: Einfuhrung in dieFarbmetrik, Kap. 6).

The expense of creating a print scale depends on the number of fields tobe measured. An acceptable expenditure is achieved when the number offields to be measured is not more than a few hundred. If scan values aregenerated for each coordinate axis of the print scale, n³ fields must bemeasured. The number of scan values must ensure a sufficiently accuratecoverage of the print scale.

In the space diagonals of the coordinate system of full colors C_(s),M_(s) and Y_(s), the proportionate basic colors of the print scale arepresent in equal amounts. With these space diagonals as the "gray axis"conclusions can be drawn as to the remaining non-linearities of theprint scale with regard to the model color space. On the basis of thedependence of the hue values on the print scale values in the "grayaxis" the minimum necessary (not equidistant) scanning steps aredetermined. The scanning steps are selected such that points areobtained along the "gray axis" that are spread as evenly as possible andat the same time at locations with as few deviations as possible betweenthe substitute colors.

Preferably, not more than seven scanning steps are stipulated. The n³scan values are then extrapolated by a cubic spline interpolation to acertain number of support points greater than the number of scanningsteps. It has been shown that a support point quantity of 32³ values isfavorable. The cubic spline interpolation results in color cubescontaining printing ink values. The subdivision of the scale space isequidistant here, i.e. a color cube with a scanning density of approx.3% is obtained in each printing ink.

The table prepared in the manner described above gives the dependence ofthe color stimulus on the printing ink proportions. The table permitsdetermination of the proportions of printing inks necessary to reproducea color stimulus.

In a preferred embodiment, the associated combinations of printing inksfor all interesting combinations of color stimuli are determinediteratively in order to generate a table giving the proportions of theprinting inks C_(s), M_(s) and Y_(s) needed to reproduce a colorstimulus, by proceeding from any point in the print scale table to firstcompute both the difference between the color stimulus required and arandom scale entry point, and the complete differential in this point inorder to ascertain a vector that gives, in scale increments, the amountand direction of the transition to another entry point better suited tothe required color stimulus. For this scale entry point appropriatecomputation steps are taken to establish a further vector that gives thetransition to a scale entry point better suited to the required colorstimulus. The computation steps for ascertaining additional scale entrypoints are repeated until the scale entry point obtained remains thesame. Color value differences still remaining are minimized by trilinearinterpolation. Using this method, which can be designated as inversion,a lookup table table for RGB or for any colors based on CIE-XYZcoordinates to CMY is obtained.

It may be that a color stimulus is required that is outside thechromaticity range of the measured print scale. The iteration processprovides for such color stimuli, for one or more colors, a dotpercentage of >100% and/or <0%. These are highly saturated colors thatcannot be reproduced. However, in order nevertheless to reproduce colorstimuli for inks outside the chromaticity range of the measured printscale, it is expedient to employ another color model based on hue,saturation and lightness (HSL color model). If the iteration processleaves the color space of the lookup table, then it is advantageous tocorrect the required color stimulus with reference to the nearest colorstimulus feasible with the lookup table. While a change in the hueshould not occur, correction may result in a substitute color having alower saturation in the case of very bright or very dark hues, andpossibly a slightly different lightness.

In order to determine the printing inks for a color stimulus outside thechromaticity range of the measured lookup table, a color spacecorresponding to the lab model stipulated by the International LightingCommission (CIE) is computed as follows for hue, saturation andlightness: ##EQU1## with X₀, Y₀ and Z₀ as the color stimulus of thewhite point (cf. DIN 6174), in which "L" means the lightness, "H" thehue, "S" the saturation and "X Y Z" the virtual primary stimuli asnormal stimuli, where the corresponding values for lightness, hue andsaturation are filed in a table with one address space for each, withstipulation of the maximum lightness value for maximum fluctuations ofthe primary stimuli and with standardization of the saturation to themaximum value occurring in the blue hues, and where for all combinationsof hue, saturation and lightness occurring, the values of the printinginks are determined by iteration and then stored. In this way, the pointat which the required color value leaves the range of the lookup tablecan only be determined as a function of the saturation. All saturationsabove this value can then be allocated the printing ink triplet of thelast color value achieved with constant lightness and constant hue.

For obtaining print results in dark hues, a black separation ispreferably generated that has been obtained using a densitometer from atest form having that number of chromatic gray bars of which eachcontains a constant black component, where the color density values areconverted to lightnesses and where a spline interpolation increases thedata density until the dependence of lightness decrease on the additionof black is given in predetermined steps for each three-color lightnesslevel. If a hue can no longer be achieved in three colors withsaturation at the predetermined lightness, transition to the nexthighest lightness level that the hue can reproduce follows, and thelightness is then reduced by addition of black to the required value.

To save on memory capacity, the lookup table of the printing inks is notaddressed directly through the measured color stimuli. The primarycolors are divided in each case into a number of classes ofrepresentative values stored in a separate table. Starting from thisseparate table, the three-dimensional table with the printing inks iscontrolled, which for that reason needs only the number of memory placescorresponding to the cubic number of the number of classes. The numberof classes is preferably adjusted to the human visual sense curve bydividing the primary stimuli into ranges of equal size under the cuberoot.

It must be noted in particular that a change in the lightness ΔL takesplace as a function of black (ΔL=f(K)).

A device for implementation of the method described above contains inaccordance with the invention a light source and a measuring head towhich is connected a spectrophotometer connected on its output side to asequential control and to a color transformer, to which is connected acubic spline interpolator controlled by the sequential control, and towhich is connected a digital memory controlled by the sequentialcontrol. The sequential control is preferably a central computer.

BRIEF DESCRIPTION OF THE DRAWINGS

Further details, advantages and features of the invention are shown notonly in the claims and in the features stated therein singly and/or incombination, but also in the following description of preferredembodiments shown in the drawings.

FIG. 1 shows a device for generation of a digital lookup table ofcomplementary printing inks in diagram form;

FIG. 2 shows a sequence diagram of process steps implemented to generatethe lookup table;

FIG. 3 shows a color chart for substitute colors in graph form,

FIGS. 4a, b show graphs of substitute colors as a function of grayvalues;

FIGS. 5a, b, c show print scale tables for the three substitute colorsas a function of the printing inks;

FIGS. 6a, b show details of the print scale tables shown in FIG. 5,

FIG. 7 shows a perspective view of a color space;

FIG. 8 shows a diagram of the lightness as a function of the saturationwith constant hue of a plane of the color space shown in FIG. 7;

FIG. 9 shows a memory subdivision in diagram form; and

FIG. 10 shows a graph of the quantization of the primary stimuli.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

For generating a digital lookup table for complementary printing inkproportions used in image reproduction equipment, a number ofmeasurement fields are provided on the test sheets (1), (2), (3). On thetest sheet (1), measurement fields numbered (4) are provided that eachconsist of the three complementary colors cyan, magenta and yellow. Theyellow component is identical for all fields of a test sheet, but variesfrom test sheet to test sheet. The color components of cyan and magentadiffer on the test sheets (1), (2), (3).

The measurement fields (4) on the test sheets (1), (2), (3) are scannedone after the other using a measuring head (5) containing a light sourceand photoelectric receiver not shown and having a spectrophotometer (6)connected behind it that is controlled by a sequential control (7). Thespectrophotometer (6) generates at its output (8) color values in theCIE standard, i.e. standard color values that are supplied to thesequential control (7) and to a color transformer (9) that generatesfrom the standard color values substitute color values or model colorvalues. The substitute color values, also known as model color values,are supplied to a cubic spline interpolator (10) controlled by thesequential control (7). The spline interpolator (10) outputs a printingink table that is filed in a digital memory (11). The spectrophotometer(8) has a color correction feature.

For printing, an image defined by RGB color pixels must be convertedinto the four color separations cyan, magenta, yellow and black. Therequired quantity ratio of printing inks is determined from an RGB datatriplet using a transformation described in detail in the following. Thebasis for generation of the transformation table of the RGB color valuesinto CMYK color values is the spectrophotometric measurement of thecolor scale on the test sheets (1), (2), (3) generated with the process(e.g. Offset, Euroskala, coated paper) for which the transformationtable is to apply. With very great expenditure, it would be possible tothereby obtain by measurement the right field for every required colorstimulus from a scale with 1% gradation of the printing inks, i.e.100*100*100 color fields. A method of this type would provide, if thecolor range of the scale is not always exceeded, the formula for CMYaccurate to 1%. Highly saturated hues have no corresponding field. Inaddition, one million measurements are impracticable for generating atable. With the invention, it is possible to describe a print scale withsufficient accuracy using a minimum of measurement fields, and to adaptnon-reproducible color stimuli to useful substitute values.

A computation model is presented whose coordinate axes tally as closelyas possible with the axes of the print scale for cyan, magenta andyellow, i.e. a component of the model color space should depend inlargely linear form on one and one only printing ink. The CIE-XYZstandard color model does not fulfill this requirement. The directionsof its coordinate axes do not even approximately tally with those of theprimary stimuli of the print scale, and identically sized colorintervals are reproduced at different points of the print scale onvariously sized differences in XYZ.

For this reason, ideal substitute colors for cyan, magenta and yellow,referred to in the following as C_(t), M_(t), Y_(t), are defined whichapproximately describe the printing ink for cyan, magenta and yellow,referred to in the following as C_(s), M_(s), Y_(s), but which can beconverted as a group into the XYZ coordinates of the standard colorchart.

FIG. 3 shows the chromaticity range of the print scale in the standardcolor chart. The primary stimuli red, green and blue, referred to in thefollowing as R, G, B, are--as is clear from FIG. 3--so positioned in themodel of the ideal substitute colors that the entire print scale (12) iswithin the triangle set up between RGB. R is on the extension of thecyan geometric locus through the white point, G on that of magenta and Bon that of yellow. This ensures an optimum separation of the colors fromone another inside the model. The relationship C_(t) =1-R makes C_(t)proportional to G_(s), and weighting with the cube root linearizes thedependence of the model color material on the printing ink.

The following apply: ##EQU2##

The conversion of RGB to XYZ and XYZ back to RGB is achieved using atransformation matrix in each case (cf. Richter Kap. 6).

To limit the expense for measurement of a print scale, it is expedientfor the number of fields to be measured not to exceed a few hundred. Ifscan values are taken in every coordinate axis, n³ fields must bemeasured. It is particularly favorable if n is not greater than 7. Inall other respects, the motto applies "The less the better" as long asthe scale is covered with sufficient accuracy.

In the space diagonal in the spatial C_(s), M_(s), Y_(s) coordinatesystem, the proportionate basic colors of the scale are present in equalamounts. These space diagonals of the "gray axis" permit conclusions tobe drawn as to the remaining non-linearities of the print scale withregard to the model color space. Based on the dependence of the huevalues on the scale values in the gray axis, the minimum necessary (notequidistant) scanning steps are therefore determined. FIGS. 4a and 4bshow two different offset scales. The first print scale is best scannedin the points 0%, 30%, 50%, 80%, 100% and combinations thereof. Theother scale requires a minimum of 6 scanning steps per coordinate (0%,30%, 45%, 70%, 85%, 100%).

To generate the lookup table, therefore, fields of the full colorsC_(s), M_(s), Y_(s) and of white are measured in a first step (13) (seeFIG. 2). In the first step (13), digital data is obtained which containsthe C_(s), M_(s), Y_(s) trajectories of the color spider. Step (13) isfollowed by step (14), in which the primary stimuli R_(t), B_(t), G_(t)of the model system for C_(t), M_(t), Y_(t) are calculated in the mannerdescribed above. The computed primary stimuli are loaded into the colortransformer (9). A step (15) is then implemented in which the spacediagonal of the print scale (12) is generated from the data obtained instep (13). For this purpose, a certain number of equidistant valuesalong the space diagonal is necessary. It has become clear that coveragein m points with m>10 is favorable. In a step (16), the space diagonalis then used to obtain the number of n scan values with which the spacediagonal is most precisely approximated to. As mentioned above, n shouldbe less than 7. The n scan values result, as mentioned above, in n³ scanvalues, which are obtained from an appropriate number of measurementfields. In the following step (17), the measuring directions for the n³measurement fields of the test sheets (1), (2), (3) are generated. Aftergeneration of the measuring directions, the device shown in FIG. 1 isused to measure and store under computer control n³ measured values oftest sheets (1), (2), (3) in a step (18). The method is continued in astep (19) in which the n³ scan values are extrapolated by cubic splineinterpolation to a larger number of support points. It has become clearthat a support point number of 32³ is favorable.

The subdivision of the scale space is equidistant here, i.e. afterinterpolation the color cube of the scale is present in every color witha scanning density of approx. 3%. It should be noted that this pigmentmay itself not even include the measured support values. The splinefunction used assumes a constant rise before the first and after thelast interval. The sequence of the colors:

1.) C from n to 32 at n×n points with constant M and Y

2.) M from n to 32 at 32×n points with constant C and Y

3.) Y from n to 32 at 32×32 points with constant C and M.

The result is printing ink tables for the various printing inks which inFIGS. 5a, b and c represent the interpolated substitute colors Y_(t),M_(t), C_(t) as a function of the printing inks Y_(s), M_(s), C_(s). Thesupport points obtained by interpolation as a function of the printinginks are entered in a step (20) into the digital memory (11) in whichthey are available under appropriate addresses.

The table interpolated from the print scale describes the dependence ofthe color stimulus on the printing ink proportions, in short:

    C.sub.t, M.sub.t, Y.sub.t (C.sub.s, M.sub.s, Y.sub.s)      (I)

In image reproduction equipment, metering of the printing inks requiresthe proportions of printing inks that must be applied to reproduce thecolor, i.e.

    C.sub.s, M.sub.s, Y.sub.s (C.sub.t, M.sub.t, Y.sub.t)      (II)

The conversion of the print table leading from (I) to (II) is referredto as inversion in the following. For all interesting combinations in astimulus system (e.g. from EBU-RGB of the European Broadcasting Union),the appropriate combination of printing inks is determined iteratively.Proceeding from any point in the scale table (referred to in thefollowing as print scale), the difference between the required colorstimulus and that of any scale entry point is first computed in additionto the complete differential in this point. This leads to a vector thatgives in scale increments the amount and direction of the transition toa new entry point better suited to the required color stimulus. Thesecomputation steps are repeated (iteration) until the entry point intothe 32*32*32 element-sized table remains constant. The remaining colorvalue differences are then minimized by linear interpolation (constantdifferential in tripod). The result is then typically a table from RGBor HSL to CMY with 64³ to 80³ entries. It must be noted that this methodonly converges onto the right end value when the prefixed signs of thedifferential quotients do not change within the model. For this reason,the scale is checked during spline interpolation for monotonously risingmodel values as the scale values increase. If this condition isinfringed by--for example--inaccuracies in both spectrophotometricmeasurements, the appropriate scan values in these non-permissibledependencies (e.g. Δ C_(t) (Δ Y_(s)) must be recorrected. The acceptanceof this secondary condition is permissible, since as a rule an increaseof one printing ink also effects an increase in the model stimuli.

In FIG. 6a, a random point (21) is shown to which the coordinate valuesc, m+1, y are allocated. The inversion process described above supplies,in accordance with FIG. 6b, the values C_(s), M_(s), Y_(s) (c, m+1, y)at point (22). Point (21) as a support point is surrounded by points notprovided with identifying numbers as additional support points. FIG. 6bshows the model values at the support points.

Inversion is implemented in accordance with the following formulas:

If the space of the print scale with the 32**3 support points isregarded in a partially linear fashion, the following applies in atripod set up at any support point for the color interval: ##EQU3##(indices s identify the print scale, t the model color space;) with##EQU4## (omit indices t at C, M, Y. c, m, y are entry points into thescale 0<c,m,y<32)

With the assumption that the step widths in the scale are constant andidentical in all direction, it follows: ##EQU5## (Δ=constant step width,corresponding to increase of printing ink/scale entry point)

From one iteration step to the next, (n→n+1), the following applies:##EQU6## as the divergence to be minimized.

It may occur that a required color stimulus is outside the chromaticityrange of the print scale measured. The iteration process provides inthis case a dot percentage of >100% and/or <0% for one or more colors.For these highly saturated colors that cannot be reproduced, substitutevalues can be ascertained. It is not permissible to extrapolate beyondthe limits of the scale, since the substitute value so obtained dependson what point of the color cube the scale is left during iteration, i.e.on the starting value. The result is discontinuities (colorfluctuations) in the case of highly saturated colors, which indicatethat a transformation of this type is not sufficient. Averagingprocesses applied subsequently to the three-dimensional table onlydisplace these faults, but do not eliminate them. To remove thisdifficulty, a transition is made to another color model, i.e. an HSLcolor model giving hue, saturation and lightness of the colors.

If the iteration process leaves the color space of the scale, therequired color stimulus can be generated by correction to the next oneobtainable using the scale.

The substitute color may have a lower saturation and, in the case ofvery bright or very dark hues, also a slightly different lightness.However, changes in the hue should not be permissible. A color spacesimilar to the CIE Lab model is defined in accordance with the inventionand converted to that model with respect to HSL (hue, saturation,lightness):

The following applies: ##EQU7##

For quantization of this color space, a table with a 20 bit addressarea, subdivided into 128 steps for lightness, 128 steps for hue and 64steps for saturation, is reserved. Assume the maximum value for L isreached for maximum fluctuations of R, G and B, and that saturation isstandardized to the maximum value occurring in the blue hues R=0, G=0,B=max. In this way, the entire range of positive EBU-RGBs is covered.

The following applies: ##EQU8##

FIG. 7 shows the color space in a perspective view, with the lightness Lshown in the vertical direction, the hues H at varying angles and thesaturation S in the horizontal direction. The values given above areentered into the color space according to FIG. 7. A triple loop is nowused, as described above, to obtain by iteration the appropriate valuesfor CMY for all HSL combinations from the high-interpolated print scale.The inner loop here always runs from 0 to maximum saturation. In thisway, the point at which the required color value leaves the scale rangecan only be found dependent on the saturation. All S values above thisare allocated the CMY triple of the last color value obtained withconstant L and H values.

The measures described above are based on scales of three-colorcomposition. Complete integration of the usual fourth color, black, inthe print scale would require the three-dimensional initial area to beprojected onto a scale of four-dimensional composition. Instead of n³fields, n⁴ would have to be measured, interpolation would extend to 32⁴fields, and inversion would have to iterate in parallel between 32 3Dspaces, assuming a secondary condition for black. Transformation tablesthus obtained would supply correct values for every degree of chromaticcolor reduction (GCR) up to complete achromatic composition.

A black separation can be generated with considerably less expense thatmeets all the requirements placed on so-called skeleton black, and alimitation of the maximum dot precentage of all colors to values fromapprox. 280% (UCR) is possible without substantial losses of naturalityof the color impression.

The HSL model is taken as the basis from which the dependence of thelightness, e.g. of the L component, on black is determined. To do so, atest form is proof-printed that contains n gray bars of chromaticcomposition. Each of these bars has a constant black component added toit in growing measure so that n "black scales" are obtained. Adensitometer is sufficient for their measurement, with only the densityvalues having to be converted into lightnesses (L). A possible colorcast of the black printing ink is not covered in these observations.

The spline interpolation already mentioned is used to increase the datadensity until the dependence of the lightness decrease on the additionof black is available in 1% steps for each lightness level composed ofthree colors. If a hue can no longer be achieved using three colors withsaturation at a predetermined L value, recourse is had to the nexthighest L level that can represent this hue, and then the lightness isreduced to the required value by the addition of black. Errors insaturation are unavoidable here, but are certainly less than thoseachievable with three-color darkening. In the diagram shown in FIG. 8,the lightness L is shown vertically. The saturation S is drawnhorizontally. The hue H is assumed to be constant. A required colorstimulus which cannot be achieved with the predetermined L value isidentified as "a". A transition follows to the next highest colorstimulus achievable, identified in FIG. 8 as "b". Then black is added toreturn to the required value of "a". This required value is identifiedwith "c". Strictly speaking, the transitions between the levels due tothe black apply only in the (measured) achromatic axis. Highly saturatedcolors might undergo a slight change in the chromatic hue or are shownslightly brighter or darker than required. The black separation therebygenerated differs from a conventional one derived from the equation

    K=gradation * Min (C.sub.s, M.sub.s, Y.sub.s)

by a moderate chromatic color reduction (GCR) and therefore by a higheraddition of black in dark, full hues. This effect is welcome, permittingas it does the somewhat purer representation of these colors. There isno hard limit to the maximum total dot area (UCR), and indeed this isnot absolutely necessary on account of the automatic withdrawal of thechromatic colors, but can be achieved subsequently by applying the usualUCR processes to the finished color pigment.

The entire RGB-CMYK conversion table must be in the main memory of thecomputer for the running time of the color reproduction system. Thismemory is generally limited, so that the direct representation of all3*8 bit RGB combinations (16 million colors) is not usually possible. Adouble table entry point is best used to remedy this. The 256 discreteamplitudes per primary color are divided by the first table into kclasses of representative values (k<256). The three-dimensionalconversion table is controlled using these classes, and containstherefore only k³ entries.

FIG. 9 shows a corresponding memory subdivision. For the primarystimulus R, a first table (23) is provided. Each further primarystimulus has a table (24) or (25). Tables (23), to (25) are used foraddressing the three-dimensional conversion table (26). To optimize thepossible dynamics of the table, the classes are selected so thatquantization is adjusted to the human visual sense curve. Based on theliterature (Munsell curve, CIE Lab), we allocate the primary stimuli tok areas of identical size under the cube root. Accordingly, a finerdefinition than 1/256 would be the result in dark hues. This is notused, so every stage of the input quantity is reproduced directly inthis part. A useful color reproduction can already be achieved withk=64, however clearly perceptible stages appear when a gray-scale wedgeis reproduced. To avoid a subsequent operation for "smoothing" of theseparations (e.g. by addition of noise), it is advisable to raise k to80. The memory capacity for the color pigment is then 2 Mbytes.

FIG. 10 shows in graph form the linear gradation as a function of theRGB quantization classes. From the colorimetric viewpoint, the colorpigment should already optimally effect the necessary transformation, sothat a subsequent modification of the CMYK separations could only worsenthe image reproduction quality.

First the scale of the reproduction process is proof-printed. Thechromatically composed gray axis of the scale is first studied. Itprovides information on the hue gradations (e.g. 5 of each) to bemeasured and that are to form the 125 support points of the scale forthe interpolation process. The (per se independent) measurement of theblack scales (approx. 25 fields) now follows.

The measurement itself is preferably performed using thespectrophotometer (6). The spectra are standardized to the standardwhite tile and assessed with the characteristics of one of theconventional light sources (D 50, D 53, D 65) and the standard spectralvalue curves of the CIE 2° standard observer for X, Y, Z. The variousstandardized light types require various centering operations forconversion to EBU-RGB, so that achromatic hues in the system have 3equal values.

In the method described above, the introduction of a model CMYcoordinate system adapted to the print scale linearizes the data, andincreases the accuracy of interpolation (two-stage system; firstmathematical approximation to the scale, and only then processing of themeasured values). The various elements of the image to be reproduced aretransformed one after the other singly from RGB or XYZ to CMY(iteration). The method can be accelerated using cache procedures.

The color range coverable in RGB is quantized into k perception-adaptedclasses per coordinate axis. For all k-possible combinations of R, G, B,the appropriate color value in CMY is (without image to be processed)determined in advance (double table access). For the running time of thecolor system, separation is therefore very fast (lookup table). Thebuildup of the lookup table is not possible with respect to the memorycapacity until requantization (k=65=80=100, 1 MB-2 MB-8 MB) has beencompleted.

The intermediate step via a hue-saturation-lightness color model allowseasy reproduction of non-reproducible colors on the surface of the CMYprinting ink pigment. It is possible here to place the error in any ofthe axes perceived as orthogonal (!) by the human visual sense. Themethod is practicable in particular thanks to the use of theperception-active classes.

Thanks to the HSL intermediate step, the influence of black (darkening,desaturation) can be described in two coordinates instead of three(ignoring the hue effects). In this way, it is possible to calculateboth a skeleton black with a correct hue value as well as thesubstitution of black for the gray component achieved by blendingchromatic colors, i.e. the hue is not dependent on the addition of blackin the first approximation.

The following applies:

    δH/δK=0

This secondary condition creates up n 3D spaces in L, S, K.

This saves the need for iteration in 4 dimensions (C, M, Y, K).

Although various minor changes and modifications might be proposed bythose skilled in the art, it will be understood that I wish to includewithin the claims of the patent warranted hereon all such changes andmodifications as reasonably come within my contribution to the art.

We claim:
 1. A method for generating a digital look-up table for threeprinting inks in image reproduction equipment from color scan valuesobtained by photoelectric scanning of originals, comprising the stepsof:measuring full colors of the three printing inks and white byscanning corresponding originals; determining model colors that have anapproximately linear relationship to the printing inks by use of aposition of a chromaticity range of a print scale having scale colors,three primary stimuli of the model colors in a chromaticity diagram eachlying on an extension of trajectories of the scale colors through awhite point, a triangle set up by lines running between said threeprimary stimuli enclosing the chromaticity range of the print scale;adjusting a scale division of the primary stimuli with a cube root to alinear gradation of the printing inks; determining a number of fields tobe scanned by using space diagonals of the printing inks as a functionof said model colors; further processing scan values of said fields tobe scanned by a cubic spline interpolation with a higher number ofsupport points for generating a look-up table; storing values of themodel colors as a function of printing ink values; making the colorstimuli for cyan, magenta and yellow for the model colors depend on theprimary colors according to the following relationships: ##EQU9##wherein the stimuli for cyan, magenta and yellow are referenced C_(t),M_(t), Y_(t) and the primary stimuli red, green and blue are referenced"R, G, B"; measuring the space diagonals at several scanning points andusing the space diagonals for determining scan values; and a cubic powerof said scan values determining a number of fields to be scanned.
 2. Amethod according to claim 1 wherein a lookup table of the printing inksas a function of the model colors is created by iteration from thelook-up table, said look-up table being stored.
 3. A method according toclaim 1 wherein a lightness/saturation/hue color model is used todetermine substitute values for colors for those colors not reproduciblein accordance with the look-up table, where values equally spaced andorthogonal according to a human visual sense curve are adjusted inlightness and saturation while retaining hue.
 4. A method according toclaim 1 wherein iteration for all combinations necessary for printing ina color stimulus system proceeds from a random point in a print scaletable and initially generates both a difference between a color stimulusrequired and any scale entry point and a complete differential in thispoint in order to ascertain a vector that gives in scale increments anamount and direction of a transition to another entry point more closelyapproximating to the required color stimulus, for said scale entry pointappropriate computation steps being taken to establish a further vectorthat gives a transition to a scale entry point better suited to therequired color stimulus, said computation steps for ascertainingadditional scale entry points being repeated until the scale entry pointobtained remains the same, and color value differences still remainingbeing minimized by linear interpolation.
 5. A method according to claim1 wherein for color stimuli outside the chromacity range of the measuredprint scale the respective color stimulus is corrected with reference toa nearest color stimulus achievable with the print scale, whileretaining hue and changing saturation, and if necessary, brightness, inaccordance with a lightness/saturation/hue model.
 6. A method accordingto claim 5 wherein the following equations apply for thelightness/saturation/hue model: ##EQU10## with X₀, Y₀ and Z₀ as thecolor stimulus of the white point, in which "L" means the lightness, "H"the hue, "S" the saturation and "X, Y, Z" virtual primary stimuli asnormal stimuli, wherein corresponding values for lightness, hue andsaturation are filed in a table with one address space for each, withstipulation of a maximum lightness value for maximum fluctuations of theprimary stimuli and with standardization of saturation to a maximumvalue occurring in blue hues, and wherein for all combinations of hue,saturation and lightness occurring, values of the printing inks aredetermined by iteration and then stored.
 7. A method according to claim1 wherein a function of a darkening process for a printing ink ispredetermined as a function of black, and wherein for a color stimuluswith a lightness not achievable by addition of the other color stimuli,black printing ink is added, with a computation following in an HSLspace.
 8. A method according to claim 7 wherein the computation assumesan orthogonality of H and K in sections in a three-dimensional sub-spaceLSK at H wherein K represents black color.
 9. A method according toclaim 1 wherein the primary colors are divided in each case into anumber of classes of representative values stored in a separate table,and wherein the values of said tables control a three-dimensional tableof the printing inks.
 10. A method according to claim 9 wherein theclasses are adjusted to a human visual sense curve.
 11. A methodaccording to claim 1 including the steps of providing a light source anda measuring head to which is connected a spectrophotometer connected atits output side to a cubic spline interpolator controlled by asequential control, to which is connected a digital memory controlled bythe sequential control.
 12. A method according to claim 11 wherein thesequential control is provided as a central computer.